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Omni-MATH / The skeletal structure of circumcircumcircumcoronene, a hydrocarbon with the…

Problem

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problem

The skeletal structure of circumcircumcircumcoronene, a hydrocarbon with the chemical formula C150H30\mathrm{C}_{150} \mathrm{H}_{30}, is shown below. Each line segment between two atoms is at least a single bond. However, since each carbon (C) requires exactly four bonds connected to it and each hydrogen (H)(\mathrm{H}) requires exactly one bond, some of the line segments are actually double bonds. How many arrangements of single/double bonds are there such that the above requirements are satisfied? If the correct answer is CC and your answer is AA, you get max(⌊30(1−|loglog2CAC|)⌋,0)\max \left(\left\lfloor 30\left(1-\left|\log _{\log _{2} C} \frac{A}{C}\right|\right)\right\rfloor, 0\right) points.
Plain-text mathematical notation (without MathML)
The skeletal structure of circumcircumcircumcoronene, a hydrocarbon with the chemical formula C₁₅₀H₃₀, is shown below. Each line segment between two atoms is at least a single bond. However, since each carbon (C) requires exactly four bonds connected to it and each hydrogen (H) requires exactly one bond, some of the line segments are actually double bonds. How many arrangements of single/double bonds are there such that the above requirements are satisfied? If the correct answer is C and your answer is A, you get max(⌊30(1−|log_(log₂C)(A)/(C)|)⌋,0) points.
Original LaTeX notation
The skeletal structure of circumcircumcircumcoronene, a hydrocarbon with the chemical formula $\mathrm{C}_{150} \mathrm{H}_{30}$, is shown below. Each line segment between two atoms is at least a single bond. However, since each carbon (C) requires exactly four bonds connected to it and each hydrogen $(\mathrm{H})$ requires exactly one bond, some of the line segments are actually double bonds. How many arrangements of single/double bonds are there such that the above requirements are satisfied? If the correct answer is $C$ and your answer is $A$, you get $\max \left(\left\lfloor 30\left(1-\left|\log _{\log _{2} C} \frac{A}{C}\right|\right)\right\rfloor, 0\right)$ points.

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Source and history

task_id
95ceea16-0bb1-5580-ae89-2ec2e76cc70e
task_key
test--95ceea16-0bb1-5580-ae89-2ec2e76cc70e
task_revision_id
1
config / split
/ test

Official source

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